Question

Докажи, что данные обыкновенной дроби можно перевести в конечные десятичные. Запиши выражение, используя десятичные дроби и выполни действия в десятичных дробях. 0,8+1/5; 1/2+2,3; 3,75-1/4; 5 1/8-3,125; 13/25*11,111; 2,002*1/2 (2в 4 степени); 9/25:0,036; 70,707:7/50. Спасибо.

Answer 1

0.8+0.2=1
0.5+2.3=2.8
3.75+0.25=4
5.125-3.125=2
0.52х11.111=5.77772
2.002*0.5*16=16.016
0.36/0.036=10
70.707/0.14=505.05

Answer 2

Proof of Conversion of Common Fractions to Decimal Fractions

To prove that common fractions can be converted to finite decimal fractions, let's convert the given fractions to decimal fractions and perform the specified operations.

1. Conversion of Fractions to Decimal Fractions: - 0.8 as a decimal fraction: 0.8. - 1/5 as a decimal fraction: 0.2. - 1/2 as a decimal fraction: 0.5. - 2.3 as a decimal fraction: 2.3. - 3.75 as a decimal fraction: 3.75. - 1/4 as a decimal fraction: 0.25. - 5 1/8 as a decimal fraction: 5.125. - 3.125 as a decimal fraction: 3.125. - 13/25 as a decimal fraction: 0.52. - 11.111 as a decimal fraction: 11.111. - 2.002 as a decimal fraction: 2.002. - 1/2 as a decimal fraction: 0.5. - 2^4 as a decimal fraction: 16. - 9/25 as a decimal fraction: 0.36. - 0.036 as a decimal fraction: 0.036. - 70.707 as a decimal fraction: 70.707. - 7/50 as a decimal fraction: 0.14.

2. Performing Operations in Decimal Fractions: - 0.8 + 1/5 = 0.8 + 0.2 = 1.0 - 1/2 + 2.3 = 0.5 + 2.3 = 2.8 - 3.75 - 1/4 = 3.75 - 0.25 = 3.5 - 5 1/8 - 3.125 = 5.125 - 3.125 = 2.0 - 13/25 * 11.111 = 0.52 * 11.111 = 5.77772 - 2.002 * 1/2 (2^4) = 2.002 * 0.5 * 16 = 16.032 - 9/25 : 0.036 = 0.36 / 0.036 = 10 - 70.707 : 7/50 = 70.707 / 0.14 = 505.05

Therefore, the given common fractions can be converted to finite decimal fractions, and the specified operations can be performed in decimal fractions.

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